Season 17, Episode 66: How Do We Know There’s One Planet Per Star on Average?

Hey StarTalkians! Season 17, episode 66 was an exoplanet-focused discussion between Neil, co-host Matt and guest Professor Evgenya Shkolnik. Early in the discussion, they discuss a fact that comes up on StarTalk a lot: that each star has at least one planet, on average.

The Habitable Worlds Observatory with Evgenya Shkolnik - StarTalk Radio

(from 4:50)

Professor Shkolnik explains how we know this briefly, but what data exactly leads to this conclusion?

The First Exoplanets We Detected

Before getting into how we came to the estimate, it’s worth looking at the early hunt for exoplanets. The first confirmed discovery came in a 1992 paper, which looked at data from a pulsar, a rapidly-rotating type of star which produces a reliable, periodic signal pulse. This particular pulsar – the not-so-memorably named PSR1257+12 – should release a pulse every 6.2 milliseconds. However, precise measurement showed an unexpected, periodic variation in timing.

Researchers realised that this was likely due to a planet. As the pulsar is tugged slightly due to planetary orbits, the pulses’ travel time to Earth varied. In fact, they determined two exoplanets were probably responsible.

A similar but more broadly-applicable method is using the same effect of planetary orbits on a more regular star. The change in star motion relative to Earth, as it’s gravitationally pulled by an exoplanet, produces a Doppler shift in the wavelength – like the apparent change in pitch as an ambulance speeds past you. The first exoplanet discovery in a main-sequence star came in 1995 using this method.

Why It’s One Planet Per Star on Average

But these are just two methods – there are many more. One of the most interesting is gravitational microlensing – the same method that will be used by the Nancy Grace Roman space telescope – which depends on the magnifying effect of small-scale gravitational lensing.

The likely source of the “one planet per star” claim is a 2012 paper which used microlensing data from two surveys, the Optical Gravitational Lensing Experiment (OGLE) and the Probing Lensing Anomalies Network (PLANET), from 2002 to 2007. As Professor Shkolnik explained, the researchers combined detections – matched across both datasets – with calculations of detection efficiency to make the estimate.

They found that in the range of between 0.5 to 10 Earth orbital distances and between 5 Earth masses and 10 Jupiter masses, every star in the Milky Way has 1.6 planets on average. They write “Planets around stars in our Galaxy thus seem to be the rule rather than the exception.”

Season 17, Episode 64: Bose-Einstein Condensates Explained

Hey StarTalkians! Episode 64 of season 17 was a “Thing You Thought You Knew” edition, where Neil educates Chuck about unintuitive physics. The episode started with a discussion of Bose-Einstein condensates:

Bose-Einstein Condensate, Collisions, The Physics of Fire –TYTYK - StarTalk Radio

But – to simplify the explanation – Neil breezes past some crucial concepts on the way. So here’s a more detailed explanation.

The Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two particles with half-integer spin (“fermions,” like electrons) can occupy the same quantum state. This is why atoms take the structure they do. With no exclusion principle, all electrons would tend towards the lowest-energy state, but the principle essentially sets a maximum occupancy. Two electrons can fit in the lowest-energy state, but only if they take opposite spin values, making two distinct quantum states.  

Bosons – named after the same Bose as the condensate – don’t obey this rule, so photons and other bosons can be indistinguishable, with identical quantum states.

De Broglie Wavelengths

As stated in the podcast, all particles have what’s called a de Broglie wavelength – they’re also waves. This is generally calculated based on the momentum of the particle or object – higher-momentum objects have smaller wavelengths. However, there is also a thermal de Broglie wavelength, which calculates this wavelength based on the temperature-related motion of molecules in a gas. Hotter gases have faster-moving particles, which in turn have smaller wavelengths.

Bose Einstein Condensation

In most cases, the de Broglie wavelengths of gas are much smaller than the distance between particles, and we can describe the gas using classical physics. But if we cool the gas a lot, down to near absolute zero, the thermal de Broglie wavelengths of neighbouring particles start to overlap, and we need quantum mechanics to describe what’s going on.

The whole picture came together when Satyendra Bose sent Einstein his derivation of the black body radiation law by treating photons as indistinguishable particles. Einstein saw the significance of this immediately, and applied it to ideal gases. In his second paper about this, he realised that after a certain amount of cooling, there would be a mysterious “condensation” from a boson gas. Since the Pauli Exclusion Principle doesn’t apply to bosons, when their thermal de Broglie wavelengths become longer than the separation between them, they condense into the same quantum state. They begin to behave as one.

Season 17, Episode 61: Why Crystal Healing is More Harmful than Helpful

Hey StarTalkians! Episode 61 of season 17 was a rare, chemistry-focused episode featuring guest Kate Biberdorf, along with Neil and Negin. Early in the discussion, they start discussing crystals, and Neil asks for a chemist’s blessing about a point he often makes:

The Chemistry of Life with Kate the Chemist - StarTalk Radio

(from 11:30)

Kate is (understandably) a little wary of criticising crystal healing to avoid offending her friends, but for a few reasons, it’s worth making the point a little more clearly than they did in the podcast.

Testing Crystal Healing

There have been surprisingly few tests of the claims of crystal healing. However, psychology professor Chris French, working with Lynn Williams and (later) Hayley O’ Donnell, conducted two widely-cited but never fully-published tests.  

French, writing in The Skeptic, explains that the test involved one real quartz crystal and one identical-looking one made of glass. In the first test, 80 participants held one of these crystals for five minutes, before reporting if they felt any of six “mildly anomalous” sensations. Half of them also read a brief primer on crystals beforehand. The results were clear: it made no difference whether participants were holding a real crystal – most of them felt one of the sensations either way. This was more likely if they were primed.

A second test was conducted a couple of years later with better blinding, and the result was basically the same, except priming didn’t make a difference this time.

There is one published test looking at crystal healing. This worked in a similar way: 138 participants were randomly assigned either a true crystal or a similar-looking placebo, and were instructed to keep it for two weeks. They completed two surveys to track anxiety symptoms before and after intervention. They were also classified as either believers in crystals or non-believers.  

The study again found that there was no apparent difference between the real and fake crystal. Regardless of which they got, believers generally felt improvements while non-believers didn’t. The authors concluded that this was likely due to conditioning and the placebo effect.

The Harm of Crystals

A common counter-argument is that crystals are ultimately harmless. However, aside from the risks of crystal healing being used for serious health problems, the industry exploits workers in low-income countries such as Madagascar, including child labour, low pay and dangerous working conditions. For consumers, crystals are “safe,” but the industry is certainly not.  

Season 17, Episode 58: Why Does String Theory Have So Many Dimensions?

Hey StarTalkians! Episode 58 of season 17 was another Cosmic Queries edition, with guest and string theorist Professor Lara Andersson, Neil and Jordan. Many of the questions concerned the – seemingly excessive – number of dimensions in string theory. This one really gets to the heart of the matter:

Quantum Anomalies with Lara Anderson - StarTalk Radio

(from 30:30)

Professor Andersson explains it very well in layman’s terms. Truthfully, it’s difficult to convey without a lot of mathematics, but here, I’ll try to address the core issue in a little more detail.

Why Does String Theory Have Extra Dimensions?

String theory is an attempt to unify all four fundamental forces – thus creating a “theory of everything.” When you’re doing this, it’s probably wise to not make any assumptions about the number of dimensions there are. After all, it’s possible that we aren’t aware of all of them.

So you can develop the ideas of string theory in a “dimension agnostic” way, just putting d in place of anything dependent on the number of dimensions.

Working this way, you eventually run into an issue. Any such theory would have to be invariant under a transformation called a Weyl transformation, but this can be broken by quantum mechanical effects. In order to form a consistent theory with these “Weyl anomalies,” they have to cancel out.

That’s when d comes back. It was found that with d = 26 (in the case of bosonic – force-related – string theory) or d = 10 (in the case of fermionic – matter related – superstring theory), you can ensure the cancellation. In this way, the dimensions kind of just come out of the theory, if it is to work at all.

How Many Extra Dimensions?

It depends on the specific theory. Five different variants of string theory quickly developed, which physicists found connections between by rescaling so-called “coupling constants” which appear in each. In 1995, Ed Witten realized that these five theories were just special cases of “M theory” – the mother of all string theories.

In M theory, there are 11 dimensions. This is therefore the best answer to how many dimensions are present in string theory.

So... Where Are They?  

As explained on the podcast, the complete lack of these dimensions in our experience is explained by “compactification.” This is questionable, from a philosophical perspective, but does fix the problem of “where are the extra dimensions?”.

Season 17, Episode 63: What is The Chronology Protection Conjecture?

Hey StarTalkians! Season 17, episode 63 features Neil and special co-host, astrophysicist Janna Levin, talking about the new StarTalk series “In Theory” and touching on a range of cosmic issues. In the discussion, they briefly mention the so-called “chronology protection conjecture” of Stephen Hawking:

In Theory with Janna Levin - StarTalk Radio

(from 32:20)

But the discussion is more focused on the nature of conjecture in physics, and it left me thinking: what really is the chronology protection conjecture?

Bending Light Cones and Time Travel

According to Einstein’s theory of relativity, the speed of light is the ultimate speed limit of the universe. If you’re at some location at time t(1), by time t(2), you can’t possibly have moved further than a photon would have been able to. This sets boundaries on the possible places you could get to, and therefore, the things you could have a causal effect on.

These boundaries are expressed as a “light cone”. Every event has a light cone in its past – the possible events that could have led to it – and one off in its future – the things it could possibly effect.

However, just like gravity warps spacetime, certain spacetime arrangements can bend your lightcone too. Imagine being close to a black hole – even if you don’t fall in, the intense gravity certainly limits how far you can possibly move.  

People have solved Einstein’s equations to show spacetimes that bend lightcones into a big loop, called closed timelike curves. If you went around such a loop, you’d end up back where and when you started the loop.

The Wormhole Time Machine

One example is a wormhole time machine, as described by Kip Thorne. If you sent one end of a wormhole moving at close to the speed of light, it would experience less time than the other end, a little like the “twin paradox”. Going through the wormhole and out of the moving end would send you back to this earlier time. But surely that’s not possible, right?

The Chronology Protection Conjecture

That’s where Hawking’s paper comes in. Although it’s technically a “conjecture” because it can’t be truly settled without a theory of quantum gravity, the paper’s argument is detailed and complex. Hawking argues that establishing such a system would lead to a build up of quantum vacuum fluctuations, to the point where the wormhole would be destroyed before it could ever be used.

Season 17, Episode 60: Next Stop, Alpha Centauri! How Light Sails Could Allow Interstellar Travel

Hey StarTalkians! Episode 60 of season 17 was a basic, Neil-and-Chuck Cosmic Queries edition, with topics ranging from fractals to the boundaries between universes. One listener asked about how we could actually make it to Alpha Centauri:

Cosmic Queries – Light Sails & Quantum Scales - StarTalk Radio

(from 17:45)

Neil brings up light sails, which is one of the most promising approaches we’ve come up with so far, and one specific project that intended to use them. Here’s how it would work.

The Physics of Light Sails

The core concept underpinning light sails is that light has momentum. The momentum (p) of a photon can be simply calculated based on its energy divided by the speed of light (p = E / c), or as Planck’s constant divided by the wavelength (p = h / λ). This is what pushes the tails of comets away from the sun, for example.

A 1971 NASA paper goes into detail about the force you’d expect from solar radiation acting on a flat surface. While there’s a lot more detail, basically the momentum comes from photons which reflect off the surface, and is strongest if the light hits perpendicular to the surface (dropping off with the square of cosine of the angle).

The Challenges of Making a Working Light Sail

Many of the key challenges were outlined a paper by Philip Lubin. In particular – and as you might guess – the actual amount of momentum from light is not huge. This means that you need two things right off the bat: as big a sail as possible, and as lightweight a craft as possible.

Lubin proposes a “spacecraft on a wafer,” and suggests boosting the power to the sail by using lasers rather than sunlight, but both aspects of this are challenging. As discussed on the podcast, he calculates that this could achieve a quarter of the speed of light in a matter of minutes.

Other serious issues include the problem of decelerating when the craft arrives at its destination.

The Failure of Breakthrough Starshot

The project Neil mentioned, though, ultimately did not achieve these goals. As detailed by Scientific American, the project intended to use a fleet of tiny spacecraft powered by laser-light to make a relatively quick 20-year journey to Alpha Centauri. The article has all the details, but the short version is that the billionaire funder seemed to lose interest.

Season 17, Episode 56: What is the Planck Length and Why Does it Matter?

Hey StarTalkians! Episode 56 of season 17 was a Cosmic Queries edition, with Neil, Chuck, Gary and astrophysicist Charles Liu. About halfway through, they received this mind-bending question:

Cosmic Queries – The Fractal Universe with Charles Liu - StarTalk Special Edition

(From 30:30)

You can tell from the strained response that this isn’t a simple matter, but it all revolves around the so-called Planck length. Beyond this limit, we’re pretty sure our theories break down. But what even is it, and why is it so significant?

Planck’s Units Explained

Planck’s constant is familiar to anyone who’s studied quantum mechanics, but it’s worth starting with Max Planck’s original idea of a new system of units. In an 1899 paper, in a short final section entitled “Natural Units of Measurement,” Planck points out the terrestrial nature of our units of measurement.

Planck was interested in proposing units that would make sense to anyone, even extraterrestrial cultures. To this end, he worked with two constants from the problem he solved in the paper (including what we now call Planck’s constant, h), along with the speed of light in a vacuum (c) and the gravitational constant (now called G).  

By combining these constants in appropriate ways, he derived values for what we now call the Planck length, the Planck mass and Planck time, as well as Planck temperature.

These values diverge from “everyday” human-world values quite a bit. For instance, while the Planck mass is closer to a useful size, the Planck length is unimaginably tiny. As Symmetry magazine explains, if a proton was the size of the observable universe, the Planck length would stretch only from Chicago to Tokyo.

The Physical Significance of Planck Units

Planck was not trying to make some bold prediction about quantum gravity when he proposed his units, but they end up central to these discussions anyway. In the 1950s physicists started to notice the Planck length cropping up in their work on quantum gravity. For example, John Archibald Wheeler investigated quantum fluctuations of the spacetime metric, and found that these fluctuations become significant at the Planck length – even though he didn’t even know about Planck’s units at the time!

As Neil stressed in the podcast, many different results like this indicate that the Planck scale is where our ideas about the universe start to break down. We’d need a theory of quantum gravity to make sense of it.

Season 17, Episode 55: Drake, Seager and Oluseyi – Are We Alone in the Universe?

Hey StarTalkians! Episode 55 of season 17 was a Cosmic Queries edition with astrophysicist Dr. Hakeem Oluseyi. While discussing his new book Why Do We Exist, Dr. Oluseyi mentions his “Oluseyi equation”:

Why Do We Exist with Hakeem Oluseyi - StarTalk Radio

(from 12:30)

Neil immediately compares it to the famous Drake equation. And despite key differences, their goals are ultimately the same. But that goal might not be what you’re thinking.

The Drake Equation Explained

Frank Drake’s equation was proposed in 1961, when the Search for Extraterrestrial Intelligence (SETI) was just getting started. It’s largely composed of a series of probabilities multiplied together.

The equation is for N, the number of civilizations in the Milky Way we may be able to communicate with. It depends on:

• The rate of star formation in the galaxy

• The fraction of stars suitable for life

• The fraction of stars with planets

• The number of planets per system that could support life

• The fraction of these that develop life

• The fraction of that life which is intelligent

• The fraction of intelligent life with the technology and desire to communicate

• How long such a civilization lasts

Dr. Oluseyi points out that this is outdated. We now know, for instance, that basically every star hosts planets. The equation is clearly geared towards the goals of SETI, with a focus on radio communication across space.

Speculation vs. Science

The Drake equation is largely speculative. How can we possibly determine the fraction of planets that develop intelligent life? It was intended more as a conversation-starter than it was a genuine piece of science [2]. The results depend strongly on how optimistic you are about these unknown questions.

Seager’s Variant and the Oluseyi Equation

Dr. Oluseyi mentions Sara Seager’s version. She switches the focus on radio signals for a more modern, grounded focus on life creating a “signature gas” which can be picked up by spectroscopy.

Dr. Oluseyi’s equation from his new book continues this tradition, focusing instead on the presence of multi-cellular life. He describes it as combining the probability of “just right” stars, “just right” planets and whether life actually occurs.

All of these – from Drake to Oluseyi – have a shared goal: to promote discussion of the search for alien life. It’s more about sparking thought than it is getting a solid number.  

Season 17, Episode 54: Galileo Proved That King Kong Would Struggle to Stand

Hey StarTalkians! Episode 54 of season 17 was a “Thing You Thought You Knew” edition, where Neil gave Chuck a crash course in sidereal days, impact craters and “the size of life.”

Why Craters Are Round, Size of Life, The Real Length of Day – TYTYK -…

(From 32:20)

The discussion on the scaling of strength and mass for animals hearkens back Galileo – and likely earlier – and leads to one unusual conclusion. Galileo proved that King Kong wouldn’t work about 300 years before the iconic monster appeared on-screen.

From Galileo to On Being the Right Size

Galileo probably came up with his idea because of a mistake he made when giving a lecture about Dante’s Inferno and the huge structure it implies. His mistake is a pretty intuitive one: if you take a structure and scale everything up equally, you’d naively expect it to still hold up just fine.

But Galileo realized there’s a problem. Imagine a chandelier hanging from a small rope that can just about hold it up. If you double every dimension of the chandelier, the volume – and mass – increases by 2 × 2 × 2 = 8 times. But the rope’s strength only comes from its cross-sectional area, i.e. the number of strands it contains. If you double every dimension of the rope, the length is useless and the strength only increases by 2 × 2 = 4 times.

The chandelier got heavier quicker than the rope got stronger, and it would come crashing down.

A famous essay by polymath J. B. S. Haldane addresses “being the right size,” and wraps Galileo’s conclusions up in a quirky-yet-informative package. He discusses some fictional giants that were ten times a human’s size in each dimension. This means 1,000 times the mass. But their legs – like the rope above – only get 100 times stronger. This means each leg would need to be working 10 times harder in a proportionally-scaled giant.  

Why King Kong is (Probably) Impossible

King Kong’s size varies in different movies, but 50 ft is an oft-used figure. This makes Kong 8.33 times bigger than a normal gorilla. This means his legs would be about 69 times stronger, but he’d weigh about 578 times more. Based on a 150 kg gorilla, Kong would weigh almost 87,000 kg, in the range of the largest sauropod dinosaurs, which had proportionally much wider legs. Even if he could stand, he certainly wouldn’t be climbing any skyscrapers.

Season 17, Episode 51: 3 Ways We’re Hunting Dark Energy, Explained

Hey StarTalkians! Episode 51 of season 17 welcomed Dr. Jason Rhodes, who sat down with Neil and Paul to discuss the new Nancy Grace Roman Space Telescope and the hunt for dark energy. This took up most of the podcast, but particularly the first half:

The Hunt for Dark Energy with Jason Rhodes - StarTalk Radio

Dr. Rhodes mentions three ways the telescope will be looking for dark energy, but as is often the case, it was easy to get lost in the meandering discussion. So here’s a briefer, clearer list.

Method 1: Type 1a Supernovae

This was discussed early on in the history of this board, but the short version is: these supernovae are “standard candles,” which are used to fix cosmic distances. If you fix the distances of many of these across different redshifts, you can tell how fast space appears to be expanding.

Method 2: Baryon Acoustic Oscillations

Baryon acoustic oscillations are a little like frozen sound waves, spread out over the universe. Back when the universe was a hot, electron-baryon plasma, photons were basically trapped. They continually interacted with the plasma, until the universe cooled enough for the particles to form into the first atoms. At this point, the photons could finally escape, leading to the well-known cosmic microwave background radiation (CMB).

But at the same time, the ripples of what happened in the plasma phase spread out too. Denser regions of the early plasma universe were pulled together by gravity, but pushed back apart by the interacting photons. This led to oscillations – like sound waves – which travelled through the plasma until the universe cooled.

These waves were released along with the CMB, and form another key relic of the early universe. A distinctive signal of this has been detected.

Like type 1a supernovae, these can be used to establish a distance scale, and any distance scale can be used to probe dark energy.

Method 3: Weak Lensing

Gravitational lensing is usually discussed in the dramatic cases, like a galaxy cluster magnifying and warping an ancient galaxy behind it. But it also operates on much smaller scales, and this type is useful in the hunts for dark matter and dark energy. This gets especially technical, but the short version is: weak lensing is useful in combination with the other two methods, and by helping to map the distribution of dark matter.